The aim of this paper is to prove that for certain generalized Weyl algebras A (including the first Weyl algebra A, over a field of characteristic zero) and for every simple left (right) A-module M, there are infinitely many non-isomorphic simple left (right) A-modules {N-i} such that Ext(A)(1)(M, N-i) not equal 0 (respectively Ext(A)(1),(N-i, M) not equal 0).